A previous question that I asked got me thinking about simultaneity, and I have a couple of questions on the subject. Concerning the Einstein's train thought experiment. The observer on the train perceives the lightning to strike the front of the train first. So in his reference frame he does not consider the two lightning strikes to be simultaneous, as the observer on the platform does. But let's say that there was a clock at the front of the train and one at the back of the train. Both clocks were knocked out by the lightning strikes. If the observer goes to restart the clocks he will realize that both clocks stopped at exactly the same time. He will also realize that the strikes were therefore simultaneous after all. Doesn't this mean that even in his reference frame the lightning strikes occured simultaneously, whether he perceived them as happening that way or not? If he's a bright guy he also realizes that this means that he must be in motion. If we do the same thing for the observer on the platform, then he too can check the clocks to verify his perception that the strikes occured simultaneously. What this leads me to wonder is.....is it possible to create a sort of temporal GPS? Could an advanced enough civilization set up a system of beacons to act as an absolute time keeper. Against which anyone can determine their position and motion, by comparing their shipboard "clock" against these beacons? I also wonder if there are any objects in the universe that could act as natural beacons, against which a space traveler could compare his perceived rate of motion? I don't know, but perhaps you could somehow employ pulsars. Just wondering.
Hi Fiziqs! No. The observer on the platform regards the clocks as showing different times. He regards the lightning as striking them at the same time on the platform clock, but at different times on "themselves". (the further apart two clocks are on the train, the bigger the difference in the times they show as seen simultaneously by the observer on the platform)
tiny-tim, I'm sorry, but I'm confused. I can understand how the observer on the train can see the two lightning strikes as happening at different times, due to the fact that the light from the rear of the train takes longer to reach him than the light from the one at the front. But if the observer actually walks to the front of the train to check the time on the clock, then walks to the rear of the train to check the time on that clock, shouldn't they be the same? I'm really confused. Maybe you can help me out though. Let's say that the observer on the train is wearing a watch. Let's assume also that he had checked the clocks at the front and back of the train at some earlier point on his trip, and found them to be in perfect synchronization. He did this by walking to both clocks, and confirming that they were indeed in agreement with his watch. He has now established that all three timepieces are synchronized. So I guess that my first question is, if after checking that they're synchronized and returning to his position at the middle of the train, what would he see? If he could somehow see the clocks at the front and rear of the train from his position in the middle, would the clocks at the front and rear still appear synhcronized? Or would the time delay be greater to the one at the rear, as opposed to the one at the front? It seems to me that it must. But I'm almost certainly wrong again. So maybe if you could explain what the observer in the middle of the train actually sees and why, it would help. How does he see the time on the front and rear clocks from his position in the middle, after having previously walked to each clock to confirm that they were synchronized? If I can understand what the observer on the train sees and why, maybe I could get my head around this problem. Thanks
Hi Fiziqs! No, that's wrong. The observer on the train (if he stands in the middle) says that the light takes the same time to reach him. It is the observer on the platform who says that the light from the rear takes longer to reach him, because he is moving away from the light. Once he has confirmed that his own watch is synchronised with each of the clocks, he will regard all three clocks as synchronised, no matter where he is standing. But then of course the observer on the platform regards the clocks as not synchronised … the lightning illuminates the clocks at the same time for him, but not when they're showing the same time (ie the same time for the observer on the train)!